## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 9

to which the

to which the

**equal**sides are opposite , shall be**equal**each to each , viz . the**angle**ABC to the**angle**DEF , and the**angle**ACB to DFE . For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight ... Page 10

FA G IE * 3 Ax . the two triangles AFC , AGB ; therefore the base FC is

FA G IE * 3 Ax . the two triangles AFC , AGB ; therefore the base FC is

**equal*** to the base GB , and the triangle AFC to the triangle AGB ; and the remaining**angles**of the one are**equal*** to the remaining**angles**of the other , each to ... Page 13

A To bisect a given rectilineal angle , that is , to divide it into two

A To bisect a given rectilineal angle , that is , to divide it into two

**equal angles**. Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in AB , and from AC cut * off AE 3. 1 . equal to AD ; join DE ... Page 15

CG : therefore the

CG : therefore the

**angle**CHF is**equal*** to the**angle*** 8. 1 . CHG ; and they are adjacent**angles**: but when a straight line , standing on another straight line , makes the adjacent**angles equal**to one another , each of them is a right ... Page 16

1 Ax . that are

1 Ax . that are

**equal**to the same thing , are**equal*** to one another ; therefore the**angles**CBE , EBD are**equal**to the**angles**DBA , ABC : but CBE , EBD are two right**angles**; therefore , DBA , ABC are together**equal**† to two right ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole